Giggs’ lack of reaction to United’s winner at Newcastle was captured on television — while by contrast van Gaal shouted and gesticulated in celebration.
Asked about their relationship, Van Gaal answered sarcastically before saying he was irritated by the questions.
He told a news conference: “No. We have a very bad relationship. I cannot answer that. I want to have those rumours.”
He then added: I am very irritated at this question because everyone can see we have a very good relationship. We work very hard together. Not only with Ryan but with all the staff and the players. It is a way of suggesting things. I am very irritated. I take my measures against the media. I am not pleased.”
United face Arsenal in the FA Cup quarter-final at Old Trafford on Monday — the first time since the 2005 final the two clubs have met in the competition.
Van Gaal said: “It is a game, 11 v 11 on a high level. Arsenal and Manchester United are placed third and fourth. It is nearly a final I think.”
Meanwhile Papiss Cisse has accepted an FA charge for spitting at United’s Jonny Evans and faces a possible seven-match ban.
Cisse’s prospective punishment is one game higher than the standard tariff for spitting, due to an earlier sending-off this season.
Newcastle managing director Lee Charnley said: “Both ourselves and Papiss agree that this kind of behaviour is not acceptable.”
Evans denies spitting at his opponent and has until 6pm today to answer his charge.